In this paper, we propose a novel channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing algorithm (SMP), which is of special interest for Millimeter Wave (mmWave) systems, since this algorithm can leverage the inherent sparseness of the mmWave channel. Our proposed algorithm will iteratively detect exact the location and the value of non-zero entries of sparse channel vector without its prior knowledge of distribution. The SMP is used to detect exact the location of non-zero entries of the channel vector, while the LSE is used for estimating its value at each iteration. Then, the analysis of the Cramer-Rao Lower Bound (CRLB) of our proposed algorithm is given. Numerical experiments show that our proposed algorithm has much better performance than the existing sparse estimators (e.g. LASSO), especially when mmWave systems have massive antennas at both the transmitters and receivers. In addition, we also find that our proposed algorithm converges to the CRLB of the genie-aided estimation of sparse channels in just a few turbo iterations.